High order moment model for polydisperse evaporating sprays towards interfacial geometry description

In this paper we propose a new Eulerian model and related accurate and robust numerical methods, describing polydisperse evaporating sprays, based on high order moment methods in size. The main novelty of this model relies on the use of fractional droplet surface moments and their ability to predict some geometrical variables of the droplet-gas interface, by analogy with the liquid-gas interface in interfacial flows. Evaporation is evaluated by using a maximum entropy (ME) reconstruction. The use of fractional moments introduces some theoretical and numerical difficulties. First, relying on a study of the moment space, we extend the ME reconstruction to the case of fractional moments. Then we propose a new high order and robust algorithm to solve the moment evolution due to evaporation, which preserves the structure of the moment space. It involves some negative order fractional moments for which a novel treatment is introduced. The present model and numerical schemes yield an accurate and stable evaluation of the moment dynamics with a minimal number of variables, as well as minimal computational cost, but also provide an additional capacity of coupling with the diffuse interface model and the transport equation of averaged geometrical interface variables, which are essential in order to describe atomization.